Digital watermarking method robust against local and global geometric distortions and projective transforms

ABSTRACT

A method of digital watermarking which can resist against local geometrical distortions such as random bending attack, global geometrical distortions as well as projective transforms, but does not necessary require the recovering of global affine transform or even the repetition of the same watermark pattern. Further, the watermark can resist common global affine transformations such as rotation, scaling, and changes of aspect ratio, cropping as well as other types of operations such as filtering, lossy compression, printing/scanning or detection of watermark in front of video, web or photo camera or any imaging device.

BACKGROUND OF THE INVENTION

The present invention relates to methods of generating and decodingwatermarks robust against local and global geometric distortions (suchas random bending and affine transforms) and projective transforms whosemain use is copyright protection of digital media such as images, videoand digital cinema.

The increasing demands of digital copyright protection market requireadequate technologies able to resist against many unintentional andintentional attacks. The digital watermarking, as a means of detectionand tracing of copyright violations, is the most attractive scenarioaccepted by many researchers and companies.

One problem with almost all current watermarking technologies is thatthey fail to recover a watermark from random bending geometricaldistortions, known as the random bending attack (RBA). The RBA was firstintroduced by F. Petitcolas et al in the benchmarking tool Stirmark tomodel printing/scanning artifacts (F. A. P. Petitcolas, R. J. Anderson,M. G. Kuhn. Attacks on copyright marking systems, in David Aucsmith(Ed), Information Hiding, Second International Workshop, IH'98,Portland, Oreg., U.S.A., Apr. 15-17, 1998, Proceedings, LNCS 1525,Springer-Verlag, ISBN 3-540-65386-4, pp. 219-239, the content of whichis incorporated herein by reference thereto). Although today'swatermarking technologies are resistant against printing/scanning,unfortunately the RBA attack still remains an essential problem foralmost all existing watermarking methods. The practical danger of thisattack is the fact that the attacker can apply it against somewatermarking technologies using the Stirmark benchmarking tool, whilepreserving visual image quality. Having removed the watermark, theattacker can commercially exploit the attacked image, thereforeviolating copyright laws.

For further background information, see M. Barni, F. Bartolini, V.Cappellini and A. Piva, “Metodo e sistema di marchiatura o cosiddettowatermarking di immagini digitali” (“A method and a system for digitalimage watermarking”), Italian Patent FI99A000090, filed April 1999, andM. Barni, F. Bartolini, V. Cappellini, A. De Rosa and A. Piva, “Metododi rivelazione di un marchio in immagini digitalis” (“A method fordetecting watermarks in digital images”), Italian Patent FI99A000091,filed April 1999, the contents of which is incorporated herein byreference thereto.

The main difficulty in dealing with the RBA comes from the basicassumption that all geometrical alterations introduced by the attackerare modeled as a global affine transform. This does not hold for the RBAwhere the introduced distortions cannot be described using only theparameters of a global affine transform. Moreover, the situation iscomplicated by the fact that many technologies (S. Pereira and T. Pun,“Fast Robust Template Matching for Affine Resistant Watermarks”, LectureNotes in Computer Science: Third International Workshop on InformationHiding, Springer, vol. 1768, pp. 199-210, 1999, Italian PatentFI99A000090, filed April, 1999, Italian Patent FI99A000091, filed April1999, Patent WO 96/36163 PCT/US96/06618, November 1996, the contents ofwhich are incorporated herein by reference thereto) are using a globaltemplate in the magnitude spectrum of the image, which does not allowthe differentiation of local alterations introduced in the case of RBA.

Several methods use the assumption about the local character of the RBA(P. Bas, J. M. Chassery and B. Maco, “Robust watermarking based on thewarping of predefined regular triangular patterns”, Proceedings of SPIE:Security and Watermarking of Multimedia Content II, San Jose, Calif.,U.S.A., January 2000, the content of which is incorporated herein byreference thereto). However, an exhaustive search is used to recoverfrom this attack. Moreover, no dedicated synchronization structure forthe estimation of local distortions is proposed in the above methods,except for exhaustive search solutions. This severely hampers the usageof such methods in commercial and on-line applications due to the highcomputational complexity of the exhaustive approach. One way to overcomethis problem is to divide the image into segments or cells, and to embedthe watermark into each segment. This has been done by Rhoads (Patent WO96/36163 PCT/US96/06618, November 1996), by Lin et al (96/36163PCT/US96/06618, November 1996 (see C. Lin, M. Wu, J. A. Bloom, I. J.Cox, M. L. Miller, Y. M. Lui, “Rotation, Scale, and TranslationResilient Public Watermarking for Images”, Proceedings of SPIE: Securityand Watermarking of Multimedia Contents II, vol. 3971, pp. 90-98, SanJose, Calif., U.S.A., January 2000) as well as by Voloshynovskiy et al(S. Voloshynovskiy, F. Deguillaume and T. Pun, 2000), the contents ofwhich are incorporated herein by reference hereto. A particular exampleof the use of this approach to watermark generation is the periodicaltiling of the same watermark. In fact the idea of repeating the samewatermark has several advantages. First, it provides resistance againstcropping. Secondly, by exploiting the periodical structure of thewatermark, one can use either the autocorrelation function (ACF) (M.Kutter, “Watermarking resistant to translation, rotation and scaling”,SPIE International Symposium on Voice, Video, and Data Communication,November 1998) or the magnitude spectrum of the Fourier transform (S.Voloshynovskiy, F. Deguillaume and T. Pun, 2000) to estimate and recoverfrom global transformations. Unfortunately, all these schemes have asignificant disadvantage that local random bending alterations and thegeneral class of projective transformations are not integrated in thewatermark detector.

The main concept of repetitive watermarking algorithms is based on thefact that if some geometrical transform is applied to the image, eachpixel of the image is treated as having the same distortions as theremaining pixels over the whole image. However, the global ACF functionor magnitude spectrum are not able to estimate the parameters of RBA.Moreover, there exist two additional typical attacks that are notcovered by the global affine model of geometric transforms, namely thegeneral class of projective transforms and local warpings. FIG. 1illustrates typical local non-linear and global attacks that cannot bedescribed using affine transform.

Therefore, what is needed is a method of Digital Watermarking that doesnot rely on the global affine model of geometrical transforms and thusprotects against local and global Geometrical Distortions and ProjectiveTransforms.

SUMMARY OF THE INVENTION

A new method of digital watermarking is provided which is resistant tolocal random bending attacks and global geometrical attacks as well asprojective transforms, yet which requires neither the use of the globalaffine transform, nor the repetition of the same watermark pattern. Themethod is not just resistant to random bending attacks but permitswatermark design so as to be resistant to common global affinetransformations such as rotation, scaling, and changes of aspect ratio,cropping as well as other types of operations such as filtering, lossycompression, printing/scanning or the recording of image by video, webor photo cameras or any imaging device.

In an advantage of the invention, a method is provided which is able toestimate and recover from local and global non-linear geometricalalterations, which include the RBA and the projective transforms, inimages or video.

In another advantage, a reference watermark is used to recover localgeometric transformation which is also encoded and, further, can be usedfor verification of the reliability of the local geometrical transformrecovery or fast detection of the watermark in the given data for theparticular key.

In another advantage, a locally periodic informative watermark is usedfor the estimation and recovery from random bending attacks, localnonlinear and projective transforms based on a local autocorrelationfunction or magnitude spectrum of a given small local region. Theperiodicity of the watermark can be extended on a global level for theestimation of global affine distortions.

In another advantage, a locally flipped informative watermark can beadditionally used for estimation and compensation for translation andcropping attacks, based on the zero-phase condition.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing typical non-linear geometricalattacks that cannot be described using global affine transform.

FIG. 2 is a schematic diagram showing an embodiment using thehierarchical algorithm of the invention.

FIG. 3 , is a schematic diagram representing a local affine transform.

FIG. 4 is a schematic diagram of an adaptive watermark decoder based-onthe reliability of the reference watermark.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring now to FIG. 1, typical non-linear geometrical attacks areshown that cannot be described using the global affine transform,namely, the RBA, the projective transforms and local warping. The methodof Digital Watermarking of the invention does not rely on the globalaffine model of geometrical transforms and thus is able to resolve manysuch attacks.

To better understand the disclosure, certain terms will be defined. Theterm “informative watermark” refers herein to the watermark whichcarries the message, and “reference watermark” refers to the watermarkwhich carries additional information about synchronization, reliabilityand detection (i.e. watermark presence/absence), thus enhancing thedetermination of the decoding reliability based on the informativewatermark only.

The approach of the method considers the geometrical transforms at thelocal hierarchical level instead of modeling them as global affinetransforms. This allows the approximation of a global projectivetransform as a juxtaposition of local affine transforms which applies toRBA as well. In the case of global affine transforms, the parameters oflocal affine transforms will be the same as the global one, thisallowing the use of the same unified approach for modeling all the abovekinds of attacks.

The problem is formulated in the context of image watermarking, but adiscussion will follow of how the algorithm can be adapted to videosignals as well.

Referring now to FIG. 2, an embodiment for the hierarchical algorithm isshown. Diagram blocks 1 to 4 represent the hierarchical sequence ofoperations that decode the watermark assuming no geometricaldistortions. Blocks 5 to 8 involve watermark extraction assuming globalaffine geometrical transforms are applied to the image. Blocks 9 to 12show steps for watermark extraction at the local level, assumingnon-linear distortions or RBA.

The algorithm of the invention uniquely applies two components: aspecially designed method for recovering from local geometricaltransforms, and a reference watermark.

The method for recovering from local geometrical transforms is anapproach which is based on the assumption that global affine orprojective transforms, as well as the RBA, can be considered as a set oflocal affine transforms. This approximation is possible due to therestricted amount of invisible distortions that can be introduced byrandom bending to keep the quality of commercial images withinacceptable ranges. Keeping in mind the high level of local correlationrequired in images, there is a limit to the tolerable amount ofdistortion. This assumption helps in designing a special type ofwatermark, encoded with some error correction code (ECC) for robustness,and a dedicated procedure for the estimation and compensation of thesegeometrical distortions. In particular, we describe here two methods forconstructing a local watermark based on the locally periodical andflipped watermark itself, or on a specially designed referencewatermark.

Referring now to FIG. 3, an estimation of local affine transform isshown, based either on a locally periodic watermark obtained by blocksrepetition using local ACF or on the windowed magnitude spectrum, or ontemplate matching at the so called microblock level, which is thesmallest complete block before flipping and repetition; in the lattercase, the template corresponds to the reference watermark positions.

Secondly, the reference watermark is a key-based sequence that can alsobe encoded using ECC, and inserted into the image proximate to theinformative watermark. This additional reference watermark helps us:

-   -   in the determination of the watermark presence or absence in the        given image for the given key;    -   as a pilot for the estimation of a channel state for the optimal        design of a matched filter in the decoder for the informative        watermark (S. Voloshynovskiy, F. Deguillaume, S. Pereira and T.        Pun, “Optimal adaptive diversity watermarking with state channel        estimation”, Proceedings of SPIE: Security and Watermarking of        Multimedia Content III, vol. 4314, San Jose, Calif. , U.S.A.,        22-25 January 2001, the content of which is incorporated herein        by reference thereto);    -   in enhancing the evaluation of the reliability of the local and        global geometrical transforms recovering; and    -   in the estimation of the reliability of the decoding of the        informative watermark.

Organized in a specific spatial structure, the informative watermarkitself can be used for the latter purpose as well. Note that thewatermark is not restricted to that of a square shape, but can also beof any regular or irregular shape that is then replicated in a specialmanner (not necessary strictly periodical) over the image.

Watermark Embedding:

The method described by Voloshynovskiy et al and detailed in the articleof S. Voloshynovskiy, F. Deguillaume and T. Pun, “Content adaptivewatermarking based on a stochastic multiresolution image modeling”,EUSIPCO2000, X European Signal Processing Conference, Tampere, Finland,September 2000, the content of which is incorporated herein by referencethereto, is suitable for this purpose because it offers a goodcompromise between the block size needed for the watermark embedding,resistance to cropping and includes an assumption about local affinetransform approximation of the RBA. Obviously, any block-basedtechnology can be adopted for this purpose. We review the stepsinvolved. We first take the message and encode it using any ECC thatperforms similarly to those described in the above paper. The codewordis then mapped from {0, 1} to {−1, 1} and encrypted by multiplying on akey-dependent sequence p with subsequent spreading over a square blockor segment of any shape with some density D using a secret key, which wecall microblock. The key-dependent reference watermark is first encodedusing the same ECC and then is added to the above microblock in theremaining spatial locations. The reference watermark includes a binarykey-dependent sequence {−1, 1} and its length is determined by theembedding density (1-D) as it is described above. The resultingmicroblock is up-sampled by a factor 2 to receive a low-pass watermarkand then flipped and copied once in each direction, producing asymmetric block, called flipped block. Obviously, non-regular upsamplingcan be used to produce groups of 2, 3, 4 or more pixels in any spatialarrangement to resist against the printing/scanning attack. Any “centerof symmetry” for the flipping, in the general case key-dependent, can bechosen to create the flipped block. Finally, the resulting flipped blockcan be replicated either over the whole image size, resulting in asymmetrical and periodical watermark at the global level, or only at thelocal level; local symmetry appears at the flipped block level, whilelocal periodicity can be seen in macroblocks containing at least 4repeated blocks—2 along each axis—as shown in FIG. 3. In the case ofblocks of square shape, the watermark can be expressed as:$\begin{matrix}{{w_{p}\left( {x,y} \right)} = {\sum\limits_{m = 0}^{K_{x} - 1}{\sum\limits_{n = 0}^{K_{y} - 1}{w\left( {{x - {mT}},{y - {nT}}} \right)}}}} & (1)\end{matrix}$where${K_{x} = {{\left\lceil \frac{M}{T} \right\rceil\quad{and}\quad K_{y}} = \left\lceil \frac{N}{T} \right\rceil}},$and M,N is the image size, T is the period of replication.

The resulting watermark can be slightly pre-distorted in such a way thatin every period the watermark can have some small affine distortion toresist against spatial averaging and removal attack based on subtractionof the estimated sign in the blocks or macroblocks. This pre-distortionwill not significantly affect the autocorrelation function or magnitudespectrum of the watermark used for the recovering of the global affinetransforms and will not interfere with the recovering of localnon-linear transforms.

Both the cover image and the watermark are first decomposed intomulti-resolution sub-band pyramids using the Wavelet transform and arethen added together using a perceptual masking applied to the watermark.A different masking is applied to the flat and textured areas in theimage. The resulting stego image is transformed in the coordinate domainor is stored in the compressed domain.. The watermark embedding can bealso transformed directly in the coordinate domain or in any othertransform domain that is used.

Watermark Extraction and Decoding:

Referring now to FIG. 4, an adaptive watermark decoder is shown, basedon the reliability of the reference watermark.

In order to extract the information, we first use either a maximumlikelihood estimator, or a penalized likelihood or minimum mean squareerror estimator. In the case when no geometrical transform has beenapplied, the message is directly decoded from the extracted watermark.If some geometrical transform was used, the extracted watermark isprocessed to invert these geometrical transforms. The generalized blockdiagram of the proposed hierarchical watermark extraction is shown inFIG. 2.

The first stage of the hierarchical approach is to recover the watermarkfrom the watermarked image assuming no geometrical attack. We firstcheck for the presence of the reference watermark in the first block(microblock, flipped block, or macroblock) starting from some referencepoint (for example the upper left image corner). This is done to have avery fast watermark decoding in the most probable case, where the imagewas not the subject of attack. If the watermark is successfully decoded,as indicated by the corresponding reliability of the reference watermarkdecoding or some check sum of the informative watermark, we stop thealgorithm and output the corresponding results. If the algorithm cannotreliably recover a watermark from the first block, as might be due tostrong lossy JPEG or JEPG2000 compressions, we perform the summation ofall blocks with the purpose of integrating, as much as possible, energyto increase the watermark-to-noise ratio and repeat the previousdecoding step. The blocks can be taken in any order. This is performedin the sequential blocks 1, 2, and 3 shown in FIG. 2, and block 4 if itwas correctly decoded.

If the watermark decoding fails in this case, the assumption is madethat some geometrical alterations were applied. Therefore, the secondhierarchical level of watermark decoding is activated. In this scenario,we assume first a global affine transform. The recovering from theglobal affine transform is performed in the blocks 5, 6, and 7, andblock 8 if it was successfully decoded (FIG. 2). The recovering from theglobal affine transform can be accomplished according to a knownalgorithm described in “Content adaptive watermarking based on astochastic multiresolution image modeling” (already mentioned). If thedecoding is successful, the algorithm is terminated and the decodedwatermark is output.

In the opposite case, the third hierarchical level is activated. Thedecoding of the watermark on this level assumes that, either a randomlocal bending attack, or projective transforms or that local warpingmight have been applied to the image. These distortions might also havebeen due to the imaging conditions such as in the case with digitalcinema (blocks 9-13 from FIG. 2).

One can use the third hierarchical level directly by omitting the twoprevious levels in the scenarios when only RBA-type attacks have beenapplied. This is the case for printing/scanning or digital cinema. Thisalternate embodiment considerably increases the algorithm timeperformance.

Recovering from Global Affine Transforms:

An important problem constraining the practical exploitation ofwatermarking technology involves the fact that existing watermarkingalgorithms are not robust against general geometrical attacks such asrotation, scaling, cropping, translation, change of aspect ratio andshearing. All these attacks can be uniquely described by a global affinetransform. An affine transform can be represented by the 4 coefficientsa,b,c,d that form the linear component matrix A, plus a translationcomponent {overscore (ν)}: $\begin{matrix}{A = {\begin{pmatrix}a & b \\c & d\end{pmatrix} + \overset{\rightarrow}{v}}} & (2)\end{matrix}$

The translation component ({overscore (ν)}) can be separately recovered,for example based on a cross-correlation between the extracted watermarkand the reference watermark mentioned above, or using the zero-phasecondition of a symmetrical watermark, and can be ignored in thefollowing developments. Therefore, an affine transform maps each pointof Cartesian coordinates (x,y) to (x′,y′), according to the formula:$\begin{matrix}{\begin{pmatrix}x^{\prime} \\y^{\prime}\end{pmatrix} = {A \cdot \begin{pmatrix}x \\y\end{pmatrix}}} & (3)\end{matrix}$where ‘.’ is the matrix product. Successive combination of n affinetransforms A₁, i=1 . . . n yields another affine transform that can beexpressed as A=A_(n)·A_(n−1)· . . . ·A₁. With respect to the originallyembedded watermark w, the resulting watermark w′_(p) after a globalaffine transform can be written as: $\begin{matrix}{{w_{p}^{\prime}\left( {x,y} \right)} = {\sum\limits_{m = 0}^{K_{x} - 1}{\sum\limits_{n = 0}^{K_{y} - 1}{w\left( {{A^{- 1}\left( {x,y} \right)}^{T} - \left( {{mT},{nT}} \right)^{T}} \right)}}}} & (4)\end{matrix}$where A is applied to all image blocks. Due to the periodicity of thewatermark used, the ACF of the watermark, as well as its magnitudespectrum, this results in a structure showing local maxima, or peaks,which is periodical as well. One can apply this method to estimate theparameters of the affine transform.Recovering from Local Non-linear Transforms:

A different situation is observed for the local non-linear transforms.Such transforms locally approximates the RBA, the projective transformsand the local warping as: $\begin{matrix}{{w_{p}^{\prime}\left( {x,y} \right)} \approx {\sum\limits_{m = 0}^{K_{x} - 1}{\sum\limits_{n = 0}^{K_{y} - 1}{w\left( {{A_{mn}^{- 1}\left( {x,y} \right)}^{T} - \left( {{mT},{nT}} \right)^{T}} \right)}}}} & (5)\end{matrix}$where A_(mn) is an approximation of the local affine transform appliedto the mn th block.

In order to determine local affine transforms, one can either use localACFs or magnitude spectrums at the macroblock level, or exploit thereference watermark information as template points at the flipped blockor microblock level as shown in FIG. 3. Any reasonable estimator can beused to estimate the parameters of the local affine transform based onthe correspondence between the reference structure and the modifiedblock.

Thus the method of the invention overcomes the problems associated withlocal non-linear geometrical distortions such as random bending attack,projective transforms and local warping. The method is based on theapproximation of all above attacks by local affine transforms. Twomethods have been disclosed which detect the local affine geometricalimage modifications based on a locally flipped and periodical watermark,and on a reference watermark. Further, a hierarchical architecture forthe decoding of the watermark has been disclosed after a sequence ofgeometrical attacks. Several alternative embodiments to the basic methodare possible, which will now be discussed.

Adaptive Watermarking Decoding:

The method already described can be used for adaptive decoding. Everybit of the encoded message can be considered as having passed through amultichannel communication system in the case of repetitive watermarkingor so-called diversity watermarking. While the algorithm which simplyperforms an addition of the bits from all microblocks to enhance thewatermark-to-noise ratio has been described, one may use the informationprovided by the reference watermark to adaptively select the blocks withthe highest reliability with respect to recovery from local geometricaldistortions. The method is easily applied since the encoded referencewatermark provides the corresponding estimation of decoding reliability.

The block-diagram of the adaptive decoder is shown in FIG. 4. After thewatermark has been globally estimated in step 14, the applied localaffine transform is estimated for one watermark block in step 15 (amicroblock, a flipped block, or a macroblock depending on which form oflocal template matching or local ACF is used). Then step 16geometrically compensates the watermark block, and step 17 attempts todecode the watermark. Checksum or reliability of the decoding isestimated in step 18, and if the watermark was correctly decoded in step19, the whole process is stopped and the watermark returned in step 20.Otherwise, the current watermark block is added to the so calledreliable watermark block in step 21 for a more accurate decoding; thereliable block, initialized to zero at the beginning, maintains aweighted average of all encountered watermark blocks which have beenconsidered to be reliable enough during the complete process, accordingto the previously introduced reliability measure. Therefore thereliability of the current block is checked in step 22, mainly based onthe reference watermark, thus helping decide whether or not to add it tothe reliable block. Then another decoding attempt is made in step 23from this reliable block, the reliability of the decoding being checkedagain in step 24; if decoding was successful in step 25, then theprocess is stopped and the watermark returned in step 26. Otherwise, ifdecoding failed at this stage, the sequence from steps 15 to 26 in thediagram is repeated for the next watermark block, and so on untilsuccessful decoding or until all the watermark blocks have beenprocessed—in step 27. Finally if, after all the decoding attempts areapplied, and yet the watermark still could not be decoded, then, in step28, the output is simply that a watermark could not be found.

Extensions to Other Data:

While we have described the algorithm for images, it is also directlyapplicable to video signals or digital cinema watermarking. In the caseof video and digital cinema, the algorithm is applied frame by frame orto at least some specific frames in the coordinate or transform domain.

Multiple variations and modifications are possible in the embodiments ofthe invention described here. Although certain illustrative embodimentsof the invention have been shown and described here, a wide range ofmodifications, changes, and substitutions is contemplated in theforegoing disclosure. In some instances, some features of the presentinvention may be employed without a corresponding use of the otherfeatures. Accordingly, it is appropriate that the foregoing descriptionbe construed broadly and understood as being given by way ofillustration and example only, the spirit and scope of the inventionbeing limited only by the appended claims.

1. A method for generating watermarked data Y based on given originaldata X, wherein a watermark W associated with the watermarked data Y,comprises a multi-bit informative watermark message and a referencewatermark associated with a key, the method comprising the steps of: (a)encoding the multi-bit message, and (b) generating the watermark W as afunction of the key, the encoded message, and the reference watermark,whereby the reference watermark acts as a reference to assist in theestimation and recovering from local and global alterations of theimage.
 2. The method of claim 1, wherein the method further whereby thegenerated watermarked data Y is visually indistinguishable from theoriginal data X.
 3. The method as claimed in claim 1, wherein themulti-bit message and the reference watermark with the associated keyare encoded using error correcting codes.
 4. The method as claimed inclaim 1, wherein the method further estimates channel state.
 5. Themethod as claimed in claim 1, wherein the method further verifiesreliability of the decoding.
 6. The method as claimed in claim 1,wherein the method further synchronizes decoding of the error correctioncodes.
 7. The method as claimed in claim 1, wherein the encodedreference watermark includes additional bits for checking reliability ofassociated watermark decoding.
 8. The method as claimed in claim 1,wherein the function uses perceptual masking while adding the watermarkW to the original data X in the coordinate of a transform domain.
 9. Themethod as claimed in claim 1, wherein the watermark is repeated andlocally pre-distorted in every block before combining it with theoriginal data X thereby obtaining generated watermarked data Y that isvisually indistinguishable from the original data X.
 10. The method asclaimed in claim 1, wherein the encoded informative and referencewatermarks comprises a regular or irregular structure within the block.11. The method as claimed in claim 1, wherein the informative andreference watermarks are used locally for the recovering from localnon-linear geometrical alterations based on local autocorrelationfunction or local windowed magnitude spectrum of a predicted watermark.12. The method as claimed in claim 1, wherein the informative andreference watermarks are locally symmetrical with respect to akey-dependent center of symmetry, achieving smaller perceptual impact,basic invariance with respect to 90 degrees rotations and flippings, andcropping and translation resynchronization based on the zero-phasecondition of the Fourier transform.
 13. The method as claimed in claim1, wherein the reference watermark is used to recover from localnon-linear geometrical alterations using template matching within asingle local microblock of the unflipped watermark.
 14. The method asclaimed in claim 1 wherein the decoded reference watermark is used forestimation of watermark reliability within a block to be added or to beadaptively weighted for combination with the resulting block forenhancement of watermark-to-noise ratio in decoder of error correctioncodes and to exclude unreliable blocks or to reduce the impact ofoutliers on the decoding process.
 15. The method as claimed in claim 1,wherein the original data X is video data, image data or digital cinemadata.
 16. The method as claimed in claim 1 applied to video data,wherein a plurality of watermarked video frames is generated.
 17. Themethod as claimed in claim 1, wherein the function operates in spatialdomain, Discrete Cosine Transform (DCT) domain, Discrete FourierTransform (DFT) domain, or Wavelet domain, or another suitable transformdomain, or some combination thereof.
 18. A computer-readable mediumencoded with a method for generating watermarked data Y based on givenoriginal data X, wherein a watermark W associated with the watermarkeddata Y, comprises a multi-bit informative watermark message and areference watermark associated with a key, the method comprising thesteps of: (c) encoding the multi-bit message, and (d) generating thewatermark W as a function of the key, the encoded message, and thereference watermark, whereby the reference watermark acts as a referenceto assist in the estimation and recovering from local and globalalterations of the image.